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A new approach to improved multiquadric quasi-interpolation by using general Hermite interpolation. (English) Zbl 1250.41001

Summary: A new approach to improve univariate multiquadric operators is surveyed. The presented scheme is obtained by using Hermite interpolating polynomials where the function is approximated by generalized LB quasi-interpolation operator. Error analysis shows that the convergence rate depends on the shape parameter \(c\). Thus, our operators could provide the desired smoothness and precision by choosing the suitable value of \(c\). The advantage of the resulting scheme is that the algorithm is simple and provides a high degree of accuracy.

MSC:

41A05 Interpolation in approximation theory
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